The model combines two ingredients, but that does not mean the brain files them separately
A Bayesian account of perception treats what you perceive as a compromise between what you expect and what your senses tell you. The expectation is the prior; the sensory evidence, expressed as a likelihood, says how probable the current signals are under different interpretations. In multisensory perception the brain also has to decide whether two signals, say a sound and a flash, come from one source or two, which is why these accounts are usually framed as Bayesian causal inference [1][2].
The key point for the question is that a model can be written as prior times likelihood without the brain necessarily storing those two pieces in separate places. The models are fitted to behavior, and a good fit tells you the computation is Bayesian-like, not where or how each ingredient is represented. So the existence of well-fitting Bayesian models is evidence for the computation, not direct evidence for independent encoding.
Changing the stimuli changes the priors, and changing the priors changes the evidence weighting
One line of reasoning holds that if priors and likelihoods were truly independent, you could manipulate one without touching the other: modify the stimuli and the priors should shift, and vice versa [1]. That logic is what makes the independence question testable at all, and it is the kind of manipulation Bayesian multisensory experiments rely on.
In an auditory-visual localization task, human performance was accounted for well by a model built from the product of unimodal likelihoods and a two-dimensional prior [4]. That is a concrete case where a prior over space and the sensory likelihoods both enter the same equation and together predict where people localize a stimulus. It shows the two ingredients are both needed to describe behavior; it does not by itself show they are computed in separate neural channels.
The prior is also not fixed. In audio-visual numerosity estimation, the tendency to over- or underestimate how many events occurred depended on the actual number of events, and the more malleable illusion was modulated by self-relevance, consistent with the self acting like a prior that pulls estimates toward areas of high personal salience [5]. A prior that shifts with social context is still a prior, but its flexibility makes a simple picture of a stored, separate prior module harder to maintain.
The brain appears to combine the two across a hierarchy rather than in one dedicated prior store
Neuroimaging work points toward a hierarchy of multisensory processes in the human brain, with a common-source prior combined with sensory evidence according to Bayes rule, and log likelihoods compared across conditions [2]. The framing there is a hierarchy that performs the inference, which fits the idea that priors and likelihoods are brought together within a processing cascade rather than kept in separate, sealed compartments.
Related work on how the two hemispheres handle multisensory signals found that observers process those signals consistent with Bayesian causal inference, extending the framework beyond the typical single-hand setups to bilateral tasks [3]. That broadens where the computation is observed, but it does not resolve whether the prior and the likelihood are represented independently at the neural level.
The honest answer is that the computation is Bayesian, while the encoding question stays open
Put together, these studies support a Bayesian description of multisensory perception in which a prior and sensory likelihoods are both required to predict behavior, and in which the prior can be reshaped by context such as social relevance [1][4][5]. The neural work is consistent with the brain performing this combination within a hierarchy of multisensory processes [2][3].
What none of this establishes is that priors and likelihoods are encoded independently, in the sense of separate neural representations that can be read out on their own. The experiments test behavior and brain responses against Bayesian models; they show the ingredients are both at work, not that they are filed apart. A reader should treat "Bayesian" here as a description of the computation, and "independent encoding" as a hypothesis the current evidence leaves unresolved.
Sources used in this answer
Humans' multisensory perception, from integration to segregation, follows Bayesian inference
Human multisensory integration and segregation are consistent with Bayesian causal-inference models in which priors and likelihoods both play a role, and manipulating stimuli or priors is proposed as a way to test their relationship.
Cortical hierarchies perform Bayesian causal inference in multisensory perception
A hierarchy of multisensory processes in the human brain is described as combining a common-source prior with sensory evidence according to Bayes rule, with log likelihoods compared across conditions.
Interhemispheric multisensory perception and Bayesian causal inference
Human observers process multisensory signals in a bilateral hand-matching task consistently with Bayesian causal inference.
Comparing Bayesian models for multisensory cue combination without mandatory integration
Human performance in an auditory-visual localization task was accounted for well by a Bayesian model using the product of unimodal likelihoods and a two-dimensional prior.
Self as a prior: The malleability of Bayesian multisensory integration to social salience
In audio-visual numerosity estimation, perceptual biases depended on event numerosity, and the more prior-malleable illusion was modulated by self-relevance, consistent with the self acting like a prior in cue integration.